Cutting devices of such kind are already known in various forms. Reference is made for example to DE 19926481 A1 and/or U.S. Pat. No. 6,230,542 B1. Reference is also made to U.S. Pat. No. 5,457,889 A. For the purpose of constructing such a device regardless of the working head, further reference is made to WO 03/084719 A2 and/or U.S. Pat. No. 7,254,982 B2.
In the known cutting devices, the support element is either conformed on the displaceable tool or fixedly attached to the mounting head. Also in the known cutting device, the bracing surfaces and abutment surfaces are designed as circular segments that are unbroken in the cutting direction on circular cutting edges. Thread shapes can only be provided transversely to the cutting plane.
Moreover, it is known from the first two publications cited in the preceding to create cutting recesses in each of the cutting tools in order to handle profiled parts for cutting.
The problem arises of cutting profiled parts effectively with such a cutting device.